Of course there is. And importance of so or so parameter highly depends on the application.

Thanks Pavel. But when you tune manually or by Ziegler–nichols method, can u obtain this settling time at time instant t=0 in simulation and the same in hardware too ?

Practically impossible. Only if the plant is of the zero order dynamics.

This is not a control problem but a physics problem: Just as you cannot make a brick disappear and instantly reappear across the room, you will not be able to make the output of the system disappear and instantly reappear at the referenced value.

Assuming that the plant has more than zero (interconnected) states and the control input has upper and lower limits on its amplitude (which is the case for most practical applications), it is impossible to reach settling time at t=0 unless the initial value of the states exactly match the reference at t=0, and there will be no overshoot. But that is of course useless.

Furthermore, if we lift the bounded control input assumption, a settling time at t=0 can be reached in theory by using a very high-gain loop. This is equivalent to using an infinite control input. However, such a loop will not be useful in practice. If we could apply an infinite control input, the insanely high gain still amplifies the noise to the point of instability.

Just in theory, the deadbeat discrete algorithm assure the reaching of setpoint in one step.

Ali Tivay, is it possible to reach a reduced settling point (not necessarily equal to zero) without any overshoot or rise time by PI/PID/PD controller?

If you want to start the simulation with already settled controller to its steady state, then you must initialize its integral state as well as the initial conditions of the process model. Assuming that the process is already in the steady state characterized by output y0 and input u0 you need to set the integral state of PI controller to u0. This is valid assuming that you are using a direct controller structure uc(s) = up(s) + uI(s) = KR*(yref(s) - y(s)) + (KR/(TI*s))*(yref(s) - y(s)).

Hi, real problems (no overshooting for a finite settling time) may even be solved for uncertain plants, see e.g.

Performance measures, performance limits and optimal PI control for the IPDT plant

M. Huba

Journal of Process Control 04/2013; 23(4):500–515.

Faster solutions are then described in

Comparing 2DOF PI and predictive disturbance observer based filtered PI control

M. Huba

Journal of Process Control 11/2013; 23(10):1379–1400.

Yet faster solutions would require dynamical feedforward, but under no circumstances the settling time may be reduced below the dead time value. Noise and uncertainties always prolong the settling time values.

If your Settling time is zero. When your process starts?, what is your sampling time?

At t=0, the system is in static condition, once its starts responding after t=0.00000...1 duration. P, PI, PD or PID any controller can be designed only for the dymanmic system, ie is varying with respect to time.  It is better you can post your question more elabarately. 

Thank you

Subrathra

For example: The sampling time is 10^-6 sec and I am tuning the PI controller manually so that I need to obtain at least 0.1 as settling time  if my simulation time is say 1 sec. I should not get any overshoot with negligible oscillation. 

Please refer to these articles:

https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller

https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance

https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design

Article From PID to Nonlinear State Error Feedback Controller

Article Improved Sliding Mode Nonlinear Extended State Observer base...

Article On the Improved Nonlinear Tracking Differentiator based Nonl...

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